Abstract The impact of the theory of punctuated equilibria on anthropology is restricted to physical anthropology because, contrary to the situation in the nineteenth and early twentieth centuries, evolutionary theory now affects only this subdiscipline of anthropology. The major impact of punctuated equilibria theory occurs in palaeoanthropology. Here it affects discussion of rates of evolution, species discrimination in the fossil record, and species longevity and stasis. The principal palaeontological approach to species is to define them by morphological differences. This is a typological interpretation of species, because unvarying types are examined. Hence species are found to be separated by unbridgeable gaps, and the speciation event itself is all important. Emphasis on the speciation event explains why so many adherents of punctuated equilibria are also cladists. The strictly dichotomous branching of lineages and concomitant extinction of the ancestral species which occurs in cladistic analysis also emphasizes speciation. The generation and study of cladograms have become all important in palaeoanthropology, and the biology and adaptations of ancient hominids have been denigrated. Phyletic lines are dealt with as if they are the units of evolution, and not populations, as can be seen in a number of recent studies of Plio/Pleistocene hominids. Population thinking had been introduced into physical anthropology in 1951, and had caused the disappearance of both the degree of difference criterion for species and schemes of static human categories. Studies of fossil and living hominids were transformed. If studies of hominid adaptation and biology originate in the demise of typological thinking, they are endangered by the reintroduction of typological thinking by adherents of punctuated equilibria. Hominids are analysed in terms of migration and gene flow, and not in terms of adaptation to changing forces of natural selection and local population transformation in situ. Hence, for both fossil and living hominids, punctuated equilibria theory reintroduces catastrophism as an explanation for change. Some adherents of punctuated equilibria have denigrated sociobiology as a quest for generalizations about behavioral evolution among unnatural (non-cladistic, hence non-evolutionary) groupings of organisms not descended from a common ancestor, This may affect physical anthropologists who analyse human and non-human primate or mammalian behaviour and ecology from a sociobiological perspective. Archaeology is still another subdiscipline of anthropology which may be influenced by punctuated equilibria theory, although this is less certainly seen than in physical anthropology. It has been claimed, for example, that the archaeological record shows long periods of stasis and sudden, rapid bursts of change in stone tool industries, which is the principal evidence of behavioral evolution throughout most of hominid existence. Similar claims have been made for Egyptian cultural history. Archaeologists, however, have not accepted these generalizations. Yet one area in which punctuated equilibria theory does seem to have influenced archaeological interpretation lies in the analysis of Pleistocene and Holocene extinctions. Here the argument is that humans may have directly or indirectly contributed to the extinction of many animal species, perhaps in a catastrophic fashion.